If I enable FileVault using a specific account on macOS Sierra, does the account have to be logged in for the initial encryption to take place or does the computer just have to be plugged in and awake even if a different user is logged in?
It depends on the specifics on how you did this. If it is an internal disk that you booted from and the file system is mounted, then the computer just have to plugged in and awake. The encryption takes place in the background even when another user is logged in to the computer!
On the other hand, if it is an external drive that you unmount when logging out, the encryption will not continue when another user logs in.
The important thing here is whether or not the file system is mounted. It doesn't really matter if the drive is external or internal, but that is just how people treat these two types of drives in practice.